line is higher than the surface, an embankment, or "filling," is

necessary.

The notes in the final column, indicate the points where the grade-line intersects the natural surface. Such are called zero points.

The distances are of importance in the computation of the earthwork. The above notes literally signify that either cut or fill is 0, at 2.87, also at 6.52.

These distances are obtained with sufficient accuracy for ordinary purposes by a measurement of the profile map. When the cuttings and fillings are recorded in the proper columns, the notes belonging to the section-level are complete.*

NOTE. It will be observed that the first set of notes on page 232, did not contain the columns for cut and fill.

The practice in keeping the notes differs with the work to be performed.

In extensive railway surveys, it is convenient to rule the pages of the note-book as in the first example; carrying out the field-notes to the extent of the surface heights, at least; then transfer to another book, the "distances," "surface heights," and "grade heights," ruling columns for "cut," "fill," and "remarks."

These transferred notes are recorded in ink, and reserved for use in mapping and computations.

*The following calculation may be employed in the more important cases. The triangles formed by the verticals (cut or fill), the grade-line, and the surface-line are similar, and give the following proportion:

Fill may be substituted for cut in the second and fourth terms.

The application to the first zero point, in the above notes, is as follows:

4.10.6 4.1 :: 100 : required dist., or 87.

In the second case in the notes, the cut necessary to the calculation is wanting, but is easily supplied, by determining the height of grade in the usual way at station 7.

Most road or canal surveys are made on several trial-lines before one is finally adopted. The profile of each line is carefully drawn, and the cost of construction approximately estimated.

When the route is finally selected, and the section levels satisfactorily completed, the exact width of the earthwork, both in excavations and embankments, is carefully staked out and the amount of material to be moved in the progress of construction, accurately measured.

The method of conducting this work is explained in the next section.

Before closing the subject of section levelling, we will consider the profile represented in the figure, and the set of field

notes appended, which are only partially completed, and which

will afford some examples for practice.

1. What is the "Height of Instrument" for the first position

of the level?

Ans. 31.032.

2. What is the height of the first T. P.?

Ans. 28.686.

3. What is the "Ht. of Inst." for the second position of the level?

4. What is the height of the second T. P.?

5. What is the "Ht. of Inst." for the third level?

6. What is the Height of Surface at 0?

Ans. 40.501.

Ans. 38.183.

position of the

Ans. 49.125.

Ans. 27.8.

11. Write the "Surface Heights" for the distances 1, 2, 4,

CROSS-SECTION LEVELLING.

55. All earthworks, whether excavation or embankment, unless held in position by retaining walls, require to be constructed with a sloping surface, the inclination of which depends upon the kind of earth.

If, in a railway-cutting, for instance, the banks which bound it be left too nearly vertical, when first constructed, the weathering influences, to which they are subjected, soon cause the material to slide down, until the whole slope gradually assumes a much lower inclination.

After a time, however, the tendency to roll or slide is checked by the friction of the particles themselves, and the slope thus formed will withstand the ordinary effects of sun, wind, and rain. The inclination thus assumed is called the "natural slope" of that kind of earth.*

Slopes are expressed mathematically by the ratio of their horizontal to their vertical dimensions, and which is called the ratio of slope.

S

E

F

In the diagram, which represents a road-cutting, the ratio of ES to AE, or of FS' to BF, is the ratio of slope.

In practice, the slope at which earthworks are allowed to stand, vary from 1 to 1, or 45°, (as in very coarse material); to 2 to 1, or 26° 34', in very fine sand.

*This slope is determined, experimentally, by drying a portion of the earth, and then pouring it from a slight elevation upon a level surface. The heap thus formed is a rather flat cone, whose sides stand at the lowest inclination they would be liable to assume under the action of atmospheric influences. The angle with the horizontal plane will be somewhere between 25° and 45°.

A slope of 1 to 1, (33° 41′), is found to be so far suitable for all ordinary excavations or embankments, that it is common, in the absence of an examination of the material, to adopt it as the ratio of slope throughout.

SETTING SLOPE STAKES.

56. It is evident that the width of natural surface of ground, required in the construction of a road, will vary with the depth of excavation or embankment.

As often, therefore, as it is found necessary to determine the depth of the cutting or filling, in the section level, it is also necessary to mark the boundaries of the width of the work, on the natural surface. This is done by stakes called Slope Stakes, and the field-work necessary to determine their position, and to measure the section taken across the road, of which the Slope Stakes indicate the boundaries, is called "CrossSection Levelling," or "Cross-Section Work."

57. A party of five may be usefully employed in setting Slope Stakes; viz., a leveller, rodman, axeman, and two tape

men.

The rod, for Cross-Section work, is a ruder instrument than that employed in the Section level. It should be at least fifteen feet long, with the feet and tenths plainly marked. It requires no target, the leveller himself reading the rod in the act of sighting.

The field-book is ruled as shown below.

Centre